dl{\displaystyle d\mathbf {l} } is the differential length vector of the current element

r^{\displaystyle \mathbf {\hat {r}} } is the unit displacement vector from the current element to the field point and

r{\displaystyle r\mathbf {} } is the distance from the current element to the field point

This formula is only true for a steady current, which means that electric charge is not building up anywhere. This is analogous to Coulombs law, which is only true for static charge distributions. When the current is not steady and charge distribution is changing, we have to add correction terms to the Biot-Savart Law. However, the Biot-Savart law is unreasonably robust, more so than Coulomb's Law. This is because most of the errors (the first-order error) will cancel out. Thus, Biot-Savart Law can be applied to cases that are clearly not steady; for example, household currents that alternate at 60 Hz.

In the special case of a charged point particle q{\displaystyle q\mathbf {} } moving at a constant velocity v{\displaystyle \mathbf {v} }, then the equation above reduces to a magnetic field approximately of the form:

This formula, however, is wrong. This is because a point charge moving in a straight line does not constitute a steady current nor a constant charge distribution, both of which are essential to magnetostatics. In particular, in this case, there is a changing electric field and an induced magnetic field that must be added to correct the above formula. Even though the equation is not precisely correct, it is a very good approximation (unreasonably good, in fact).